## On the Fault Tolerance of Some Popular Bounded-Degree Networks (1992)

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Venue: | SIAM Journal on Computing |

Citations: | 44 - 7 self |

### BibTeX

@INPROCEEDINGS{Leighton92onthe,

author = {Tom Leighton and Bruce Maggs and R. Sitaraman},

title = {On the Fault Tolerance of Some Popular Bounded-Degree Networks},

booktitle = {SIAM Journal on Computing},

year = {1992},

pages = {542--552}

}

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### Abstract

In this paper, we analyze the ability of several bounded-degree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an N-node butterfly containing N 1\Gammaffl worst-case faults (for any constant ffl ? 0) can emulate a fault-free butterfly of the same size with only constant slowdown. Similar results are proved for the shuffleexchange graph. Hence, these networks become the first connected boundeddegree networks known to be able to sustain more than a constant number of worst-case faults without suffering more than a constant-factor slowdown in performance. We also show that an N-node butterfly whose nodes fail with some constant probability p can emulate a fault-free version of itself with a slowdown of 2 O(log N) , which is a very slowly increasing function of N . The proofs of these results combine the technique of redundant computation with new algorithms for (packet) routing around faults in hypercubic networks. Tech...